Sort of. It's all a matter of licensing. Technically, you might own the hardware, but you are licensing the OS running on it.
A better argument would be if you took your iOS device and wrote your own stack for it. In that case, I don't think Apple would have much claim to what you could/could not run on "your" hardware. But in the current scenario you're buying iron-wrapped software (or I guess plastic-and-glass-wrapped software). Apple is really controlling what happens with the software, not the hardware.
This is an importnat distinction, IMO, because I don't believe any of the "I paid for it so it's mine" arguments out there really pass muster until you also create your own (not jailbroken) software stack.